Q110 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics

$\int\left[(\log 2 x)^2+2 \log 2 x\right] d x=$

  • A
    $(\log 2 x)^2+c$
  • B
    $2 x \log 2 x+c$
  • Correct answer
    C
    $x(\log 2 x)^2+c$
  • D
    $2 x(\log x)^2+c$

Solution

$\begin{aligned} & \mathrm{I}=\int\left[(\log 2 x)^2+2 \log 2 x\right] d x=\int(\log 2 x)^2 d x+2 \int \log 2 x d x \\ I= & x(\log 2 x)^2-2 \int \log 2 x d x+2 \int \log 2 x d x+c \\ I= & x(\log 2 x)^2+c\end{aligned}$

Hence, the correct answer is option: 'C'.

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